Evaluation of Bi-modular Behavior of Rocks Subjected to Uniaxial Compression and Brazilian Tensile Testing

It is typical for rock material to be bi-modularity in terms of Young’s modulus and Poisson’s ratio. In other words, these values differ in compression ( $$E_{{\text{c}}} ,\upsilon_{c}$$ ) and in tension ( $$E_{{\text{t}}} {,}\upsilon_{{\text{t}}}$$ ). In this work, four kinds of rock materials (sandstone, marble, granite, basalt) were tested to study such bi-modularity behavior in uniaxial compression and in tension (Brazilian disc test). The compressive elastic constants were determined from uniaxial compression testing, while the tensile elastic constants were determined by an improved methodology using displacement measurement in both horizontal and vertical directions of points on the flat surface of a Brazilian disc. Digital image correlation (DIC) was used to monitor the strain and displacement field on the Brazilian disc surface. Validation of the reliability of the testing method is also carried out, and it is found that tensile cracks initiate at the disc center for all tested specimens. Then, the rationality of the determined tensile elastic constants is validated by comparison with the values obtained from the direct tensile tests. Finally, based on the experimental data, it is found that the values of $${{E_{{\text{t}}} } \mathord{\left/ {\vphantom {{E_{{\text{t}}} } {E_{{\text{c}}} }}} \right. \kern-\nulldelimiterspace} {E_{{\text{c}}} }}$$ and $${{\upsilon_{{\text{t}}} } \mathord{\left/ {\vphantom {{\upsilon_{{\text{t}}} } {\upsilon_{{\text{c}}} }}} \right. \kern-\nulldelimiterspace} {\upsilon_{{\text{c}}} }}$$ of each rock type are similar, except for marble. As the ratio of tensile to compressive strength increases, the value of $${{E_{{\text{t}}} } \mathord{\left/ {\vphantom {{E_{{\text{t}}} } {E_{{\text{c}}} }}} \right. \kern-\nulldelimiterspace} {E_{{\text{c}}} }}$$ also appears to increase slightly. Lastly, the mechanism of bi-modular behavior of rock is discussed.